Angular Momentum and Static Equilibrium - University Physics I | PHYS 2050, Quizzes of Physics

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PHYS 2050

Fall 2011 Quiz #9 - Angular Momentum and Static Equilibrium Instructions: answer both problems and show all relevant work needed to find solution. Circle your final answer. Some (possibly) useful equations and constants Translational Σ F = m a! Ff = μkN# Ff ≤ μsN v = v 0 + at v^2 = v 02 + 2aΔx Δx = v 0 t + ½at^2 p = m v T = ve dM/dt ! Rotational v = r × ω vT = rω ω = ω 0 + αt ω^2 = ω 02 + 2αΔθ Δθ = ω 0 t + ½αt^2 Ihoop = MR^2 Isphere = 0.4MR^2 Icyl = ½MR^2 I = Σmiri^2 I = ∫r^2 dm I = Icm + MR^2 Σ τ = I α! ac = v^2 /r τ = r × F τ = rFsin θ L = r× p L = rpsin θ Energy W = ΔK Ktrans = ½mv^2 Krot = ½Iω^2 W = F·d W = ∫ F· d r ΔEsystem = ΔK+ΔU+ΔEint ΔEint = Fkd Wconservative = -ΔU P = dE/dt Ug = mgh Us = ½kx^2 Collisions v1f = v1i(m 1 - m 2 )/(m 1 + m 2 ) + v2i(2m 2 )/(m 1 + m 2 ) v2f = v1i(2m 1 )/(m 1 + m 2 ) + v2i(m 2 -m 1 )/(m 1 + m 2 ) Constants g = 9.8 m/s^2 Problems:

1. (10 pts ) A chunk of clay (mass, m ) is thrown at a solid cylinder (mass, M and radius, R ) that is rotating with an angular velocity ω ( ω > 0) about a fixed axis running through its center of mass. The clay is thrown horizontally along a line that is a distance d above the cylinder’s center. With what speed must the clay be thrown if it is to bring the cylinder to rest after it collides and sticks to the cylinder? Give your answer in terms of the aforementioned quantities.
2. (10 pts) A sign of uniform weight Fs and width 2L hangs from a horizontal beam of weight, Fb, hinged at the wall and supported by a cable. (A) Draw a free body diagram for the beam. (B) Find the tension in the cable in terms of L , d , Fs , Fb , and θ.